Unifying Lazy and Strict Computations

Non-strict sequential computations describe imperative programs that can be executed lazily and support infinite data structures. Based on a relational model of such computations we investigate their algebraic properties. We show that they share many laws with conventional, strict computations. We develop a common theory generalising previous algebraic descriptions of strict computation models including partial, total and general correctness and extensions thereof. Due to non-strictness, the iteration underlying loops cannot be described by a unary operation. We propose axioms that generalise the binary operation known from omega algebra, and derive properties of this new operation which hold for both strict and non-strict computations. All algebraic results are verified in Isabelle using its integrated automated theorem provers.

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